D.M. Kilgour

The graph model for conflicts

The graph model for conflicts is developed as a comprehensive methodology for realistically analyzing real world conflicts. The graph form takes outcomes, rather than individual decisions, as the basic units for describing a conflict. In the graph form, many solution concepts can be formulated for both two-player and multiplayer games. In particular, specific mathematical criteria are presented for categorizing solution concepts which can be used for predicting equilibria in n-player games. One of the criteria on which this taxonomy of solution concepts is based is the number of steps ahead a player may think, in terms of the reactions of other players to his actions. Other criteria include which players take part in the sanctioning process, and whether sanctioning moves are restricted to those which lead to immediate improvements for the mover. In order to demonstrate the insight which decision makers can gain from studying a dispute using the graph model, various solution concepts are applied to an important environmental engineering problem.

A decision support system for interactive decision making-Part I: model formulation

A comprehensive decision support system, GMCR II, is developed for the systematic study of real-world interactive decision problems. Model formulation is presented in Part I, and analysis and output interpretation in Part II. GMCR II is based upon existing and new research developments of the graph model for conflict resolution. In Part I, specially designed data structures and corresponding algorithms are implemented for generating and representing possible states, removing infeasible states, coalescing indistinguishable states, and specifying and storing allowable state transitions. Algorithms implementing different approaches to the elicitation of preferences over states enable GMCR II to construct and manage an efficient, flexible, and complete graph model of a strategic conflict.

A decision support system for interactive decision making - Part II: analysis and output interpretation

For pt.I see ibid., p.42-55 (2003). The development of a comprehensive decision support system, GMCR II, for the systematic study of real-world interactive decision problems is presented. The companion paper (Part I), discusses how GMCR II elicits, stores, and manages conflict models; here (Part II), the focus is on GMCR IIs analysis and output interpretation subsystems. Specifically, this paper describes the powerful and efficient analysis engine contained in GMCR II, its informative output presentation and interpretation facilities, and a number of follow-up analyses. Furthermore, an illustrative case study is used to demonstrate how GMCR II can be conveniently applied in practice.

Preference uncertainty in the graph model for conflict resolution

A new preference structure is introduced into the graph model for conflict resolution. This structure can handle a decision-makers (DM) strict preference for one state or scenario over another, equal preference for states, and uncertain or unknown preference in the comparison of two states. Built upon this preference structure, four types of solution definitions modeling human behavior under conflict are extended to accommodate uncertainty in preferences. Four distinct ways to consider uncertain preference information are identified, producing sixteen extended stability definitions. Interrelationships of these definitions within and across the four definition sets are investigated. Illustrative examples of two-DM and multi-DM conflict models are presented to show how the new solution concepts can be applied in practice.

Environmental conflict resolution using the graph model

The graph model for conflict resolution is employed to study systematically the bargaining that took place during the appeal of an environmental control order. Uniroyal Chemicals Ltd. appealed the order issued following the discovery of significant levels of the carcinogen NDMA in the water supply of the town of Elmira, Canada. NDMA was a by-product of Uniroyals production process, but direct evidence of discharges from these processes into the aquifer was lacking. These environmental negotiations were analyzed as a strategic conflict using the decision support system GMCR. The formal modeling and analysis were carried out while the negotiations were in process; the results of the study can now be compared to the actual outcome.<<ETX>>

Multiple-Criteria Sorting Using Case-Based Distance Models With an Application in Water Resources Management

A case-based distance model to solve sorting problems in multiple-criteria decision analysis (MCDA) is developed, and its application in water resources management is presented. The sorting problem in MCDA is to arrange a set of alternatives into ordered groups. MCDA is introduced as consequence-based preference aggregation, whereby consequence and preference expressions (values and weights) are defined and combined in a sequence of steps. Then, sorting problems are defined, and some properties are explained. Based on weighted Euclidean distance, two case-based distance models are developed for sorting using weights and group thresholds obtained by assessment of a case set provided by a decision maker (DM). This case-based method can elicit the DMs preferences more expeditiously and accurately than direct inquiry. Case-based sorting model I is designed for cardinal criteria, while its extension, i.e., case-based sorting model II, can handle both cardinal and ordinal criteria. Optimization programs are employed to find the most descriptive weights and group thresholds. A case study in which Canadian municipalities are sorted according to water usage is presented.

Systematic policy development to ensure compliance to environmental regulations

More efficient enforcement of environmental regulations would enhance environmental conditions around the globe by improving compliance to existing regulations and by allowing regulatory agencies to broaden their scope without increasing their budgets. This research analyzes comply-evade decisions by regulated firms in the context of their relationships with environmental agencies, and determines which enforcement policies effectively encourage voluntary compliance. More specifically, the enforcement conflict is modeled as a 2/spl times/2 non-cooperative game called the Enforcement Dilemma. This game is examined as a simultaneous game, and also as a more realistic sequential game with asymmetric information. Then a supergame based on the Enforcement Dilemma is developed and analyzed. An effective long-term policy called the review strategy is proposed to overcome the dilemma in this context. >

Representing ordinal preferences in the decision support system GMCR II

Preference information about states, or possible scenarios, is required in modeling multiple-participant decision processes. In the decision support system GMCR II, a flexible methodology is presented for conveniently eliciting a decision makers relative preferences. More specifically, when states are defined in terms of discrete option choices, three techniques are available for ordering the states from most to least preferred, with ties permitted. One method is option weighting, in which weights are assigned to each option choice, and total weights used to determine an ordering of states. A second technique is to employ an option prioritizing scheme, based upon a set of lexicographic statements. Subsequently, one can rank the states manually using a process called fine tuning. When the number of states is not too large, one may wish to order them directly and thereby skip the option weighting and option prioritizing procedures. Application of these approaches to obtain and represent ordinal preference information allows GMCR II to model real-world conflicts expeditiously, and analyze them effectively.

Water supply planning under interdependence of actions: Theory and application

An ongoing water supply planning problem in the Regional Municipality of Waterloo, Ontario, Canada, is studied to select the best water supply combination, within a multiple-objective framework, when actions are interdependent. The interdependencies in the problem are described and shown to be essential features. The problem is formulated as a multiple-criteria integer program with interdependent actions. Because of the large number of potential actions and the nonconvexity of the decision space, it is quite difficult to find nondominated subsets of actions. Instead, a modified goal programming technique is suggested to identify promising subsets. The appropriateness of this technique is explained, and the lessons learned in applying it to the Waterloo water supply planning problem are described.

Scenario generation and reduction in the decision support system GMCR II

The most difficult environmental decision problems usually involve a range of interest groups, each with different preferences with respect to scenarios, or possible states of the interaction. The graph model for conflict resolution was designed to study systematically strategic conflicts that can arise in environmental management and elsewhere. A new decision support system called GMCR II is being developed to enable practitioners to apply the graph model for conflict resolution conveniently and expeditiously. At the model building stage of GMCR II, it is often useful to represent a conflict in option form, which structures the model by specifying the decision-makers (DMs), the courses of action or options available to each DM, and each DMs preferences. If there are m options in the model, there are 2/sup m/ mathematically possible states. Usually, however, many of the possible option combinations cannot occur in practice and therefore must be eliminated from the model. The design of GMCR IIs user-friendly interface and the efficient algorithms it uses to eliminate infeasible states are presented. In addition, all states in a group of essentially equivalent states can be readily combined into one using other built-in procedures. An environmental management dispute is used to illustrate the application of GMCR II.